What is (x+x/(x-1))/(x-x/(x-1)) ?

The solution to (x+x/(x-1))/(x-x/(x-1)) is x/(x-2)

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simplify (x+x/(x-1))/(x-x/(x-1))

simplify

\frac{x + \frac{x}{x - 1}}{x - \frac{x}{x - 1}}

\frac{x}{x - 2}

Solution steps

\frac{x + \frac{x}{x - 1}}{x - \frac{x}{x - 1}}

Join

x + \frac{x}{x - 1} : \frac{x ^{2}}{x - 1}

= \frac{\frac{x ^{2}}{x - 1}}{x - \frac{x}{x - 1}}

Join

x - \frac{x}{x - 1} : \frac{x ^{2} - 2 x}{x - 1}

= \frac{\frac{x ^{2}}{x - 1}}{\frac{x ^{2} - 2 x}{x - 1}}

Apply the fraction rule:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

= \frac{x ^{2} ( x - 1 )}{( x - 1 ) ( x ^{2} - 2 x )}

Cancel

\frac{x ^{2} ( x - 1 )}{( x - 1 ) ( x ^{2} - 2 x )} : \frac{x}{x - 2}

= \frac{x}{x - 2}

\frac{2}{5} \div \frac{1}{8}

w^{2} - 18 w + 81

x^{2} - 5 x^{3}

\frac{10}{8}

What is (x+x/(x-1))/(x-x/(x-1)) ?
The solution to (x+x/(x-1))/(x-x/(x-1)) is x/(x-2)